LMFDB - Embedded newform 616.2.bi.b.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(13,616)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("616.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bi (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.37515625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - x^{6} + 3x^{5} - x^{4} + 6x^{3} - 4x^{2} - 8x + 16 $ x^8 - x^7 - x^6 + 3x^5 - x^4 + 6x^3 - 4x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			349.1
Root			$-1.41264 + 0.0667372i$ of defining polynomial
Character	$\chi$	$=$	616.349
Dual form			616.2.bi.b.293.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41264 - 0.0667372i) q^{2} +(1.99109 + 0.188551i) q^{4} +(2.51626 + 0.817582i) q^{7} +(-2.80011 - 0.399234i) q^{8} +(2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(-1.41264 - 0.0667372i) q^{2} +(1.99109 + 0.188551i) q^{4} +(2.51626 + 0.817582i) q^{7} +(-2.80011 - 0.399234i) q^{8} +(2.42705 - 1.76336i) q^{9} +(0.0629004 + 3.31603i) q^{11} +(-3.50000 - 1.32288i) q^{14} +(3.92890 + 0.750845i) q^{16} +(-3.54623 + 2.32901i) q^{18} +(0.132447 - 4.68855i) q^{22} +2.56038 q^{23} +(-1.54508 - 4.75528i) q^{25} +(4.85595 + 2.10232i) q^{28} +(-2.42225 + 7.45492i) q^{29} +(-5.50000 - 1.32288i) q^{32} +(5.16497 - 3.05338i) q^{36} +(2.31678 + 0.752769i) q^{37} +12.8185 q^{43} +(-0.500000 + 6.61438i) q^{44} +(-3.61689 - 0.170873i) q^{46} +(5.66312 + 4.11450i) q^{49} +(1.86529 + 6.82061i) q^{50} +(-1.57760 - 2.17138i) q^{53} +(-6.71939 - 3.29390i) q^{56} +(3.91928 - 10.3695i) q^{58} +(7.54878 - 2.45275i) q^{63} +(7.68122 + 2.23580i) q^{64} -10.4916i q^{67} +(12.9884 + 9.43662i) q^{71} +(-7.50000 + 3.96863i) q^{72} +(-3.22254 - 1.21801i) q^{74} +(-2.55285 + 8.39541i) q^{77} +(10.3127 + 14.1942i) q^{79} +(2.78115 - 8.55951i) q^{81} +(-18.1079 - 0.855469i) q^{86} +(1.14774 - 9.31035i) q^{88} +(5.09796 + 0.482763i) q^{92} +(-7.72535 - 6.19024i) q^{98} +(6.00000 + 7.93725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9}+O(q^{10}) $ 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9	$ 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9} + 4 q^{11} - 28 q^{14} - q^{16} - 3 q^{18} - 9 q^{22} + 16 q^{23} + 10 q^{25} - 7 q^{28} - 4 q^{29} - 44 q^{32} - 9 q^{36} + 30 q^{37} + 24 q^{43} - 4 q^{44} - 23 q^{46} + 14 q^{49} - 5 q^{50} + 50 q^{53} - 7 q^{56} + 2 q^{58} - 9 q^{64} + 48 q^{71} - 60 q^{72} - 28 q^{74} - 14 q^{77} + 40 q^{79} - 18 q^{81} - 12 q^{86} + 17 q^{88} - 24 q^{92} - 7 q^{98} + 48 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9 + 4 * q^11 - 28 * q^14 - q^16 - 3 * q^18 - 9 * q^22 + 16 * q^23 + 10 * q^25 - 7 * q^28 - 4 * q^29 - 44 * q^32 - 9 * q^36 + 30 * q^37 + 24 * q^43 - 4 * q^44 - 23 * q^46 + 14 * q^49 - 5 * q^50 + 50 * q^53 - 7 * q^56 + 2 * q^58 - 9 * q^64 + 48 * q^71 - 60 * q^72 - 28 * q^74 - 14 * q^77 + 40 * q^79 - 18 * q^81 - 12 * q^86 + 17 * q^88 - 24 * q^92 - 7 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41264	−	0.0667372i	−0.998886	−	0.0471903i
$2$	−1.41264	−	0.0667372i	−0.998886	−	0.0471903i
$3$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$3$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$4$	1.99109	+	0.188551i	0.995546	+	0.0942755i
$5$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$5$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$6$		0			0
$7$	2.51626	+	0.817582i	0.951057	+	0.309017i
$7$	2.51626	+	0.817582i	0.951057	+	0.309017i
$8$	−2.80011	−	0.399234i	−0.989988	−	0.141151i
$9$	2.42705	−	1.76336i	0.809017	−	0.587785i
$10$		0			0
$11$	0.0629004	+	3.31603i	0.0189652	+	0.999820i
$11$	0.0629004	+	3.31603i	0.0189652	+	0.999820i
$12$		0			0
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$	−3.50000	−	1.32288i	−0.935414	−	0.353553i
$15$		0			0
$16$	3.92890	+	0.750845i	0.982224	+	0.187711i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$	−3.54623	+	2.32901i	−0.835853	+	0.548953i
$19$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$19$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$20$		0			0
$21$		0			0
$22$	0.132447	−	4.68855i	0.0282378	−	0.999601i
$23$	2.56038			0.533877			0.266938	−	0.963714i	$-0.413988\pi$
$23$	2.56038			0.533877			0.266938	+	0.963714i	$0.413988\pi$
$24$		0			0
$25$	−1.54508	−	4.75528i	−0.309017	−	0.951057i
$26$		0			0
$27$		0			0
$28$	4.85595	+	2.10232i	0.917688	+	0.397302i
$29$	−2.42225	+	7.45492i	−0.449801	+	1.38434i	0.427331	+	0.904095i	$0.359454\pi$
$29$	−2.42225	+	7.45492i	−0.449801	+	1.38434i	−0.877132	+	0.480249i	$0.840546\pi$
$30$		0			0
$31$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$31$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$32$	−5.50000	−	1.32288i	−0.972272	−	0.233854i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	5.16497	−	3.05338i	0.860828	−	0.508897i
$37$	2.31678	+	0.752769i	0.380877	+	0.123754i	0.493197	−	0.869918i	$-0.335828\pi$
$37$	2.31678	+	0.752769i	0.380877	+	0.123754i	−0.112320	+	0.993672i	$0.535828\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$41$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$42$		0			0
$43$	12.8185			1.95480			0.977399	−	0.211402i	$-0.0678028\pi$
$43$	12.8185			1.95480			0.977399	+	0.211402i	$0.0678028\pi$
$44$	−0.500000	+	6.61438i	−0.0753778	+	0.997155i
$45$		0			0
$46$	−3.61689	−	0.170873i	−0.533282	−	0.0251938i
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$		0			0
$49$	5.66312	+	4.11450i	0.809017	+	0.587785i
$50$	1.86529	+	6.82061i	0.263792	+	0.964580i
$51$		0			0
$52$		0			0
$53$	−1.57760	−	2.17138i	−0.216700	−	0.298263i	0.686803	−	0.726844i	$-0.259014\pi$
$53$	−1.57760	−	2.17138i	−0.216700	−	0.298263i	−0.903503	+	0.428581i	$0.859014\pi$
$54$		0			0
$55$		0			0
$56$	−6.71939	−	3.29390i	−0.897917	−	0.440165i
$57$		0			0
$58$	3.91928	−	10.3695i	0.514627	−	1.36158i
$59$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$59$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$60$		0			0
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$		0			0
$63$	7.54878	−	2.45275i	0.951057	−	0.309017i
$64$	7.68122	+	2.23580i	0.960153	+	0.279475i
$65$		0			0
$66$		0			0
$67$		−	10.4916i		−	1.28175i	−0.767644	−	0.640877i	$-0.778571\pi$
$67$		−	10.4916i		−	1.28175i	0.767644	−	0.640877i	$-0.221429\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.9884	+	9.43662i	1.54144	+	1.11992i	0.949425	+	0.313993i	$0.101667\pi$
$71$	12.9884	+	9.43662i	1.54144	+	1.11992i	0.592014	+	0.805928i	$0.298333\pi$
$72$	−7.50000	+	3.96863i	−0.883883	+	0.467707i
$73$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$73$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$74$	−3.22254	−	1.21801i	−0.374613	−	0.141590i
$75$		0			0
$76$		0			0
$77$	−2.55285	+	8.39541i	−0.290924	+	0.956746i
$78$		0			0
$79$	10.3127	+	14.1942i	1.16027	+	1.59698i	0.710235	+	0.703964i	$0.248589\pi$
$79$	10.3127	+	14.1942i	1.16027	+	1.59698i	0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	2.78115	−	8.55951i	0.309017	−	0.951057i
$82$		0			0
$83$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$83$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$84$		0			0
$85$		0			0
$86$	−18.1079	−	0.855469i	−1.95262	−	0.0922476i
$87$		0			0
$88$	1.14774	−	9.31035i	0.122350	−	0.992487i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$		0			0
$92$	5.09796	+	0.482763i	0.531499	+	0.0503315i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$97$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$98$	−7.72535	−	6.19024i	−0.780378	−	0.625308i
$99$	6.00000	+	7.93725i	0.603023	+	0.797724i
$100$	−2.17979	−	9.75953i	−0.217979	−	0.975953i
$101$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$101$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$102$		0			0
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$		0			0
$105$		0			0
$106$	2.08367	+	3.17266i	0.202384	+	0.308156i
$107$	−3.46496	−	10.6641i	−0.334971	−	1.03093i	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−3.46496	−	10.6641i	−0.334971	−	1.03093i	0.631766	−	0.775159i	$-0.282330\pi$
$108$		0			0
$109$	−15.6273			−1.49683			−0.748414	−	0.663232i	$-0.769184\pi$
$109$	−15.6273			−1.49683			−0.748414	+	0.663232i	$0.769184\pi$
$110$		0			0
$111$		0			0
$112$	9.27225	+	5.10152i	0.876145	+	0.482048i
$113$	−3.34450	−	10.2933i	−0.314624	−	0.968314i	−0.975909	−	0.218179i	$-0.929988\pi$
$113$	−3.34450	−	10.2933i	−0.314624	−	0.968314i	0.661285	−	0.750135i	$-0.270012\pi$
$114$		0			0
$115$		0			0
$116$	−6.22856	+	14.3867i	−0.578307	+	1.33577i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.9921	+	0.417159i	−0.999281	+	0.0379235i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−10.8274	+	2.96106i	−0.964580	+	0.263792i
$127$	−6.06090	+	8.34211i	−0.537818	+	0.740242i	−0.988297	−	0.152545i	$-0.951253\pi$
$127$	−6.06090	+	8.34211i	−0.537818	+	0.740242i	0.450479	+	0.892787i	$0.351253\pi$
$128$	−10.7016	−	3.67100i	−0.945895	−	0.324473i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	−0.700180	+	14.8208i	−0.0604864	+	1.28033i
$135$		0			0
$136$		0			0
$137$	−13.7856	−	10.0158i	−1.17778	−	0.855708i	−0.185861	−	0.982576i	$-0.559507\pi$
$137$	−13.7856	−	10.0158i	−1.17778	−	0.855708i	−0.991920	+	0.126868i	$0.959507\pi$
$138$		0			0
$139$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$139$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$140$		0			0
$141$		0			0
$142$	−17.7181	−	14.1973i	−1.48687	−	1.19141i
$143$		0			0
$144$	10.8596	−	5.10570i	0.904970	−	0.425475i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	4.47100	+	1.93566i	0.367514	+	0.159111i
$149$	−17.7984	−	12.9313i	−1.45810	−	1.05937i	−0.983853	−	0.178979i	$-0.942720\pi$
$149$	−17.7984	−	12.9313i	−1.45810	−	1.05937i	−0.474247	−	0.880392i	$-0.657280\pi$
$150$		0			0
$151$	−23.2633	+	7.55872i	−1.89314	+	0.615120i	−0.916597	+	0.399811i	$0.869076\pi$
$151$	−23.2633	+	7.55872i	−1.89314	+	0.615120i	−0.976546	+	0.215308i	$0.930924\pi$
$152$		0			0
$153$		0			0
$154$	4.16654	−	11.6893i	0.335750	−	0.941951i
$155$		0			0
$156$		0			0
$157$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$157$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$158$	−13.6208	−	20.7395i	−1.08362	−	1.64995i
$159$		0			0
$160$		0			0
$161$	6.44258	+	2.09332i	0.507747	+	0.164977i
$162$	−4.50000	+	11.9059i	−0.353553	+	0.935414i
$163$	−8.29696	−	11.4198i	−0.649868	−	0.894467i	0.349225	−	0.937039i	$-0.386445\pi$
$163$	−8.29696	−	11.4198i	−0.649868	−	0.894467i	−0.999093	+	0.0425718i	$0.986445\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$167$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$168$		0			0
$169$	4.01722	−	12.3637i	0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$	25.5228	+	2.41694i	1.94609	+	0.184290i
$173$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$173$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$174$		0			0
$175$		−	13.2288i		−	1.00000i
$176$	−2.24269	+	13.0756i	−0.169049	+	0.985608i
$177$		0			0
$178$		0			0
$179$	−4.15763	+	1.35090i	−0.310756	+	0.100971i	−0.460243	−	0.887793i	$-0.652238\pi$
$179$	−4.15763	+	1.35090i	−0.310756	+	0.100971i	0.149487	+	0.988764i	$0.452238\pi$
$180$		0			0
$181$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$181$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$182$		0			0
$183$		0			0
$184$	−7.16935	−	1.02219i	−0.528531	−	0.0753570i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.80563	+	8.63483i	−0.203008	+	0.624795i	0.796781	+	0.604268i	$0.206534\pi$
$191$	−2.80563	+	8.63483i	−0.203008	+	0.624795i	−0.999789	+	0.0205267i	$0.993466\pi$
$192$		0			0
$193$	−16.2839	+	22.4128i	−1.17214	+	1.61331i	−0.524305	+	0.851530i	$0.675675\pi$
$193$	−16.2839	+	22.4128i	−1.17214	+	1.61331i	−0.647834	+	0.761781i	$0.724325\pi$
$194$		0			0
$195$		0			0
$196$	10.5000	+	9.26013i	0.750000	+	0.661438i
$197$	−2.03059			−0.144674			−0.0723369	−	0.997380i	$-0.523046\pi$
$197$	−2.03059			−0.144674			−0.0723369	+	0.997380i	$0.523046\pi$
$198$	−7.94612	−	11.6129i	−0.564706	−	0.825292i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	2.42794	+	13.9322i	0.171681	+	0.985153i
$201$		0			0
$202$		0			0
$203$	−12.1900	+	16.7781i	−0.855572	+	1.17759i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.21418	−	4.51486i	0.431915	−	0.313805i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	23.3570	−	16.9698i	1.60796	−	1.16825i	0.738490	−	0.674264i	$-0.235539\pi$
$211$	23.3570	−	16.9698i	1.60796	−	1.16825i	0.869469	−	0.493987i	$-0.164461\pi$
$212$	−2.73174	−	4.62089i	−0.187616	−	0.317364i
$213$		0			0
$214$	4.18305	+	15.2957i	0.285947	+	1.04559i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	22.0758	+	1.04293i	1.49516	+	0.0706358i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$223$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$224$	−12.7579	−	7.82540i	−0.852421	−	0.522856i
$225$	−12.1353	−	8.81678i	−0.809017	−	0.587785i
$226$	4.03762	+	14.7639i	0.268579	+	0.982082i
$227$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$227$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$228$		0			0
$229$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$229$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$230$		0			0
$231$		0			0
$232$	9.75883	−	19.9075i	0.640698	−	1.30699i
$233$	12.4411	+	17.1237i	0.815042	+	1.12181i	0.990526	+	0.137326i	$0.0438509\pi$
$233$	12.4411	+	17.1237i	0.815042	+	1.12181i	−0.175484	+	0.984482i	$0.556149\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.4127	+	3.70821i	−0.738226	+	0.239864i	−0.653907	−	0.756575i	$-0.726871\pi$
$239$	−11.4127	+	3.70821i	−0.738226	+	0.239864i	−0.0843185	+	0.996439i	$0.526871\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	15.5557	+	0.144287i	0.999957	+	0.00927509i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$251$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$252$	15.4928	−	3.46031i	0.975953	−	0.217979i
$253$	0.161049	+	8.49030i	0.0101251	+	0.533781i
$254$	9.11858	−	11.3799i	0.572151	−	0.714038i
$255$		0			0
$256$	14.8725	+	5.89998i	0.929529	+	0.368749i
$257$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$257$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$258$		0			0
$259$	5.21418	+	3.78832i	0.323993	+	0.235395i
$260$		0			0
$261$	7.26675	+	22.3648i	0.449801	+	1.38434i
$262$		0			0
$263$		−	23.0900i		−	1.42379i	−0.702284	−	0.711897i	$-0.747836\pi$
$263$		−	23.0900i		−	1.42379i	0.702284	−	0.711897i	$-0.252164\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	1.97820	−	20.8898i	0.120838	−	1.27604i
$269$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$269$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$270$		0			0
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$		0			0
$273$		0			0
$274$	18.8056	+	15.0687i	1.13609	+	0.910334i
$275$	15.6715	−	5.42265i	0.945025	−	0.326998i
$276$		0			0
$277$	26.9284	−	19.5646i	1.61797	−	1.17552i	0.803679	−	0.595063i	$-0.202873\pi$
$277$	26.9284	−	19.5646i	1.61797	−	1.17552i	0.814289	−	0.580460i	$-0.197127\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.08226	−	1.48960i	0.0645620	−	0.0888620i	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	1.08226	−	1.48960i	0.0645620	−	0.0888620i	0.840077	+	0.542467i	$0.182510\pi$
$282$		0			0
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$	24.0818	+	21.2382i	1.42899	+	1.26025i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−15.6815	+	6.48777i	−0.924040	+	0.382296i
$289$	−5.25329	−	16.1680i	−0.309017	−	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$293$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$294$		0			0
$295$		0			0
$296$	−6.18672	−	3.03277i	−0.359596	−	0.176276i
$297$		0			0
$298$	24.2797	+	19.4550i	1.40648	+	1.12700i
$299$		0			0
$300$		0			0
$301$	32.2546	+	10.4802i	1.85912	+	0.604066i
$302$	33.3671	−	9.12520i	1.92006	−	0.525096i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−6.66593	+	16.2347i	−0.379826	+	0.925058i
$309$		0			0
$310$		0			0
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$		0			0
$313$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$313$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$314$		0			0
$315$		0			0
$316$	17.8572	+	30.2065i	1.00455	+	1.69925i
$317$	−16.7792	−	23.0946i	−0.942415	−	1.29712i	−0.954815	−	0.297200i	$-0.903947\pi$
$317$	−16.7792	−	23.0946i	−0.942415	−	1.29712i	0.0123997	−	0.999923i	$-0.496053\pi$
$318$		0			0
$319$	−24.8731	−	7.56333i	−1.39263	−	0.423465i
$320$		0			0
$321$		0			0
$322$	−8.96134	−	3.38707i	−0.499396	−	0.188754i
$323$		0			0
$324$	7.15144	−	16.5184i	0.397302	−	0.917688i
$325$		0			0
$326$	10.9585	+	16.6857i	0.606934	+	0.924138i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$			32.6029i			1.79202i	0.444038	+	0.896008i	$0.353545\pi$
$331$			32.6029i			1.79202i	−0.444038	+	0.896008i	$0.646455\pi$
$332$		0			0
$333$	6.95035	−	2.25831i	0.380877	−	0.123754i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−33.3558	−	10.8380i	−1.81701	−	0.590381i	−0.999904	−	0.0138879i	$-0.995579\pi$
$337$	−33.3558	−	10.8380i	−1.81701	−	0.590381i	−0.817102	−	0.576493i	$-0.804421\pi$
$338$	−6.50000	+	17.1974i	−0.353553	+	0.935414i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	10.8859	+	14.9832i	0.587785	+	0.809017i
$344$	−35.8931	−	5.11757i	−1.93523	−	0.275921i
$345$		0			0
$346$		0			0
$347$	−14.9958	−	10.8951i	−0.805016	−	0.584878i	0.107366	−	0.994220i	$-0.465758\pi$
$347$	−14.9958	−	10.8951i	−0.805016	−	0.584878i	−0.912381	+	0.409342i	$0.865758\pi$
$348$		0			0
$349$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$349$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$350$	−0.882850	+	18.6874i	−0.0471903	+	0.998886i
$351$		0			0
$352$	4.04074	−	18.3214i	0.215372	−	0.976532i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	5.96339	−	1.63086i	0.315175	−	0.0861936i
$359$	−3.64987	−	1.18591i	−0.192633	−	0.0625901i	0.211112	−	0.977462i	$-0.432292\pi$
$359$	−3.64987	−	1.18591i	−0.192633	−	0.0625901i	−0.403745	+	0.914872i	$0.632292\pi$
$360$		0			0
$361$	−15.3713	+	11.1679i	−0.809017	+	0.587785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$367$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$368$	10.0595	+	1.92245i	0.524387	+	0.100215i
$369$		0			0
$370$		0			0
$371$	−2.19437	−	6.75359i	−0.113926	−	0.350629i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−13.4361	+	18.4932i	−0.690165	+	0.949931i	−1.00000		0.000859657i	$-0.999726\pi$
$379$	−13.4361	+	18.4932i	−0.690165	+	0.949931i	0.309834	+	0.950791i	$0.399726\pi$
$380$		0			0
$381$		0			0
$382$	4.53960	−	12.0107i	0.232266	−	0.614518i
$383$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$383$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$384$		0			0
$385$		0			0
$386$	24.4990	−	30.5745i	1.24697	−	1.55620i
$387$	31.1111	−	22.6035i	1.58147	−	1.14900i
$388$		0			0
$389$	37.4816	+	12.1785i	1.90039	+	0.617475i	0.963338	+	0.268290i	$0.0864585\pi$
$389$	37.4816	+	12.1785i	1.90039	+	0.617475i	0.937054	+	0.349185i	$0.113542\pi$
$390$		0			0
$391$		0			0
$392$	−14.2147	−	13.7820i	−0.717951	−	0.696094i
$393$		0			0
$394$	2.86849	+	0.135516i	0.144513	+	0.00682721i
$395$		0			0
$396$	10.4500	+	16.9351i	0.525131	+	0.851021i
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$		0			0
$399$		0			0
$400$	−2.50000	−	19.8431i	−0.125000	−	0.992157i
$401$	24.7856	+	18.0078i	1.23773	+	0.899265i	0.997445	−	0.0714367i	$-0.0227584\pi$
$401$	24.7856	+	18.0078i	1.23773	+	0.899265i	0.240287	+	0.970702i	$0.422758\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	18.3398	−	22.8879i	0.910190	−	1.13591i
$407$	−2.35048	+	7.72987i	−0.116509	+	0.383155i
$408$		0			0
$409$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$409$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−9.07969	+	5.96315i	−0.446243	+	0.293073i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−32.8480	+	10.6730i	−1.60091	+	0.520169i	−0.967333	−	0.253507i	$-0.918416\pi$
$421$	−32.8480	+	10.6730i	−1.60091	+	0.520169i	−0.633581	+	0.773676i	$0.718416\pi$
$422$	−34.1275	+	22.4134i	−1.66130	+	1.09107i
$423$		0			0
$424$	3.55057	+	6.70995i	0.172431	+	0.325864i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−4.88834	−	21.8865i	−0.236287	−	1.05792i
$429$		0			0
$430$		0			0
$431$	−22.6942	−	31.2358i	−1.09314	−	1.50458i	−0.844177	−	0.536065i	$-0.819910\pi$
$431$	−22.6942	−	31.2358i	−1.09314	−	1.50458i	−0.248963	−	0.968513i	$-0.580090\pi$
$432$		0			0
$433$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$433$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$434$		0			0
$435$		0			0
$436$	−31.1155	−	2.94655i	−1.49016	−	0.141114i
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	21.0000			1.00000
$442$		0			0
$443$	−39.6801	+	12.8928i	−1.88526	+	0.612557i	−0.901582	+	0.432608i	$0.857593\pi$
$443$	−39.6801	+	12.8928i	−1.88526	+	0.612557i	−0.983676	+	0.179949i	$0.942407\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	17.5000	+	11.9059i	0.826797	+	0.562500i
$449$	33.0711	−	24.0276i	1.56072	−	1.13393i	0.625310	−	0.780376i	$-0.284972\pi$
$449$	33.0711	−	24.0276i	1.56072	−	1.13393i	0.935413	−	0.353556i	$-0.115028\pi$
$450$	16.5543	+	13.2648i	0.780378	+	0.625308i
$451$		0			0
$452$	−4.71840	−	21.1256i	−0.221935	−	0.993663i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.33490	−	5.96648i	0.202778	−	0.279100i	−0.695501	−	0.718525i	$-0.744818\pi$
$457$	4.33490	−	5.96648i	0.202778	−	0.279100i	0.898279	+	0.439425i	$0.144818\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	23.0299			1.07029			0.535145	−	0.844760i	$-0.320257\pi$
$463$	23.0299			1.07029			0.535145	+	0.844760i	$0.320257\pi$
$464$	−15.1143	+	27.4709i	−0.701662	+	1.27530i
$465$		0			0
$466$	−16.4319	−	25.0198i	−0.761195	−	1.15902i
$467$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$		0			0
$469$	8.57775	−	26.3996i	0.396084	−	1.21902i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.806287	+	42.5064i	0.0370731	+	1.95445i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.65785	−	2.48818i	−0.350629	−	0.113926i
$478$	16.3695	−	4.47670i	0.748722	−	0.204760i
$479$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$479$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−21.9649	−	1.24197i	−0.998405	−	0.0564531i
$485$		0			0
$486$		0			0
$487$	−12.7279	−	39.1724i	−0.576755	−	1.77507i	−0.630123	−	0.776495i	$-0.716996\pi$
$487$	−12.7279	−	39.1724i	−0.576755	−	1.77507i	0.0533681	−	0.998575i	$-0.483004\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.5967	+	41.8465i	−0.613613	+	1.88851i	−0.193249	+	0.981150i	$0.561903\pi$
$491$	−13.5967	+	41.8465i	−0.613613	+	1.88851i	−0.420363	+	0.907356i	$0.638097\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.9670	+	34.3641i	1.11992	+	1.54144i
$498$		0			0
$499$	0.232351	+	0.0754955i	0.0104015	+	0.00337964i	0.314213	−	0.949352i	$-0.398259\pi$
$499$	0.232351	+	0.0754955i	0.0104015	+	0.00337964i	−0.303812	+	0.952732i	$0.598259\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$	−22.1166	+	3.85423i	−0.985153	+	0.171681i
$505$		0			0
$506$	0.339115	−	12.0045i	0.0150755	−	0.533664i
$507$		0			0
$508$	−13.6407	+	15.4671i	−0.605209	+	0.686242i
$509$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$509$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$510$		0			0
$511$		0			0
$512$	−20.6157	−	9.32709i	−0.911092	−	0.412203i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−7.11292	−	5.69951i	−0.312524	−	0.250422i
$519$		0			0
$520$		0			0
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$	−8.77273	−	32.0783i	−0.383972	−	1.40403i
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$		0			0
$525$		0			0
$526$	−1.54096	+	32.6179i	−0.0671893	+	1.42221i
$527$		0			0
$528$		0			0
$529$	−16.4444			−0.714976
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−4.18861	+	29.3776i	−0.180920	+	1.26892i
$537$		0			0
$538$		0			0
$539$	−13.2876	+	19.0379i	−0.572336	+	0.820019i
$540$		0			0
$541$	15.9284	−	11.5726i	0.684814	−	0.497546i	−0.190138	−	0.981757i	$-0.560893\pi$
$541$	15.9284	−	11.5726i	0.684814	−	0.497546i	0.874951	+	0.484211i	$0.160893\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−13.5967	−	41.8465i	−0.581355	−	1.78923i	−0.613440	−	0.789741i	$-0.710215\pi$
$547$	−13.5967	−	41.8465i	−0.581355	−	1.78923i	0.0320849	−	0.999485i	$-0.489785\pi$
$548$	−25.5599	−	22.5417i	−1.09186	−	0.962932i
$549$		0			0
$550$	−22.5000	+	6.61438i	−0.959403	+	0.282038i
$551$		0			0
$552$		0			0
$553$	14.3445	+	44.1478i	0.609990	+	1.87736i
$554$	−39.3457	+	25.8406i	−1.67164	+	1.09786i
$555$		0			0
$556$		0			0
$557$	13.4223	−	41.3094i	0.568719	−	1.75034i	−0.0879152	−	0.996128i	$-0.528020\pi$
$557$	13.4223	−	41.3094i	0.568719	−	1.75034i	0.656634	−	0.754209i	$-0.271980\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.62825	+	2.03204i	−0.0686835	+	0.0857163i
$563$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$563$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	13.9962	−	19.2641i	0.587785	−	0.809017i
$568$	−32.6015	−	31.6090i	−1.36793	−	1.32628i
$569$	40.2601	−	13.0813i	1.68779	−	0.548397i	0.701395	−	0.712773i	$-0.252561\pi$
$569$	40.2601	−	13.0813i	1.68779	−	0.548397i	0.986398	+	0.164375i	$0.0525608\pi$
$570$		0			0
$571$	−46.5287			−1.94717			−0.973583	−	0.228332i	$-0.926673\pi$
$571$	−46.5287			−1.94717			−0.973583	+	0.228332i	$0.926673\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.95601	−	12.1753i	−0.164977	−	0.507747i
$576$	22.5852	−	8.11833i	0.941051	−	0.338264i
$577$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$577$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$578$	6.34199	+	23.1901i	0.263792	+	0.964580i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	7.10114	−	5.36796i	0.294099	−	0.222318i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$587$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	8.53719	+	4.69710i	0.350876	+	0.193049i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	−33.0000	−	29.1033i	−1.35173	−	1.19212i
$597$		0			0
$598$		0			0
$599$	−36.4997	−	26.5186i	−1.49134	−	1.08352i	−0.973676	−	0.227937i	$-0.926802\pi$
$599$	−36.4997	−	26.5186i	−1.49134	−	1.08352i	−0.517663	−	0.855584i	$-0.673198\pi$
$600$		0			0
$601$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$601$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$602$	−44.8646	−	16.9572i	−1.82855	−	0.691126i
$603$	−18.5004	−	25.4637i	−0.753396	−	1.03696i
$604$	−47.7447	+	10.6638i	−1.94270	+	0.433903i
$605$		0			0
$606$		0			0
$607$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$607$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	3.73325	+	11.4898i	0.150784	+	0.464067i	0.997709	−	0.0676456i	$-0.0215487\pi$
$613$	3.73325	+	11.4898i	0.150784	+	0.464067i	−0.846925	+	0.531712i	$0.821549\pi$
$614$		0			0
$615$		0			0
$616$	10.5000	−	22.4889i	0.423057	−	0.906103i
$617$	3.84770			0.154902			0.0774512	−	0.996996i	$-0.475322\pi$
$617$	3.84770			0.154902			0.0774512	+	0.996996i	$0.475322\pi$
$618$		0			0
$619$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$619$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−15.5241	+	47.7782i	−0.618003	+	1.90202i	−0.299528	+	0.954087i	$0.596829\pi$
$631$	−15.5241	+	47.7782i	−0.618003	+	1.90202i	−0.318475	+	0.947931i	$0.603171\pi$
$632$	−23.2099	−	43.8626i	−0.923240	−	1.74476i
$633$		0			0
$634$	22.1617	+	33.7441i	0.880154	+	1.34015i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	34.6319	+	12.3442i	1.37109	+	0.488712i
$639$	48.1636			1.90532
$640$		0			0
$641$	7.65550	+	23.5612i	0.302374	+	0.930611i	0.980644	+	0.195799i	$0.0627300\pi$
$641$	7.65550	+	23.5612i	0.302374	+	0.930611i	−0.678270	+	0.734813i	$0.737270\pi$
$642$		0			0
$643$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$643$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$644$	12.4331	+	5.38275i	0.489932	+	0.212110i
$645$		0			0
$646$		0			0
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	−11.2048	+	22.8572i	−0.440165	+	0.897917i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−14.3668	−	24.3023i	−0.562648	−	0.951750i
$653$	42.1152	+	13.6840i	1.64809	+	0.535498i	0.978326	−	0.207072i	$-0.0663936\pi$
$653$	42.1152	+	13.6840i	1.64809	+	0.535498i	0.669768	+	0.742571i	$0.266394\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	44.0000			1.71400			0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000			1.71400			0.856998	+	0.515319i	$0.172327\pi$
$660$		0			0
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	2.17582	−	46.0561i	0.0845658	−	1.79002i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−9.96904	+	2.72632i	−0.386293	+	0.105643i
$667$	−6.20189	+	19.0874i	−0.240138	+	0.739069i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	9.76533	+	13.4408i	0.376426	+	0.518106i	0.954633	−	0.297784i	$-0.0962476\pi$
$673$	9.76533	+	13.4408i	0.376426	+	0.518106i	−0.578208	+	0.815890i	$0.696248\pi$
$674$	46.3964	+	17.5362i	1.78712	+	0.675468i
$675$		0			0
$676$	10.3299	−	23.8599i	0.397302	−	0.917688i
$677$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$677$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$			51.0901i			1.95491i	0.211147	+	0.977454i	$0.432280\pi$
$683$			51.0901i			1.95491i	−0.211147	+	0.977454i	$0.567720\pi$
$684$		0			0
$685$		0			0
$686$	−14.3779	−	21.8923i	−0.548953	−	0.835853i
$687$		0			0
$688$	50.3625	+	9.62468i	1.92005	+	0.366938i
$689$		0			0
$690$		0			0
$691$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$691$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$692$		0			0
$693$	8.60820	+	24.8777i	0.326998	+	0.945025i
$694$	20.4565	+	16.3916i	0.776518	+	0.622215i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	2.49430	−	26.3397i	0.0942755	−	0.995546i
$701$	−15.7423	−	48.4499i	−0.594579	−	1.82993i	−0.556810	−	0.830640i	$-0.687975\pi$
$701$	−15.7423	−	48.4499i	−0.594579	−	1.82993i	−0.0377695	−	0.999286i	$-0.512025\pi$
$702$		0			0
$703$		0			0
$704$	−6.93082	+	25.6118i	−0.261215	+	0.965281i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−23.0896	+	31.7802i	−0.867150	+	1.19353i	0.112667	+	0.993633i	$0.464061\pi$
$709$	−23.0896	+	31.7802i	−0.867150	+	1.19353i	−0.979817	+	0.199896i	$0.935939\pi$
$710$		0			0
$711$	50.0589	+	16.2651i	1.87736	+	0.609990i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−8.53295	+	1.90583i	−0.318891	+	0.0712244i
$717$		0			0
$718$	5.07680	+	1.91885i	0.189464	+	0.0716108i
$719$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$719$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$720$		0			0
$721$		0			0
$722$	22.4594	−	14.7504i	0.835853	−	0.548953i
$723$		0			0
$724$		0			0
$725$	39.1928			1.45559
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−8.34346	−	25.6785i	−0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$		0			0
$736$	−14.0821	−	3.38707i	−0.519073	−	0.124849i
$737$	34.7905	−	0.659926i	1.28152	−	0.0243087i
$738$		0			0
$739$	26.4857	−	19.2430i	0.974291	−	0.707864i	0.0178655	−	0.999840i	$-0.494313\pi$
$739$	26.4857	−	19.2430i	0.974291	−	0.707864i	0.956425	+	0.291977i	$0.0943129\pi$
$740$		0			0
$741$		0			0
$742$	2.64914	+	9.68682i	0.0972530	+	0.355614i
$743$	−3.79415	+	5.22220i	−0.139194	+	0.191584i	−0.872923	−	0.487858i	$-0.837778\pi$
$743$	−3.79415	+	5.22220i	−0.139194	+	0.191584i	0.733729	+	0.679442i	$0.237778\pi$
$744$		0			0
$745$		0			0
$746$	31.0780	+	1.46822i	1.13785	+	0.0537553i
$747$		0			0
$748$		0			0
$749$		−	29.6664i		−	1.08399i
$750$		0			0
$751$	12.3593	+	38.0379i	0.450996	+	1.38802i	0.875772	+	0.482724i	$0.160353\pi$
$751$	12.3593	+	38.0379i	0.450996	+	1.38802i	−0.424777	+	0.905298i	$0.639647\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−13.6240	−	18.7519i	−0.495174	−	0.681548i	0.486158	−	0.873871i	$-0.338398\pi$
$757$	−13.6240	−	18.7519i	−0.495174	−	0.681548i	−0.981332	+	0.192323i	$0.938398\pi$
$758$	20.2145	−	25.2275i	0.734224	−	0.916303i
$759$		0			0
$760$		0			0
$761$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$761$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$762$		0			0
$763$	−39.3224	−	12.7766i	−1.42357	−	0.462545i
$764$	−7.21437	+	16.6637i	−0.261007	+	0.602873i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	−36.6487	+	41.5557i	−1.31901	+	1.49562i
$773$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$773$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$774$	−45.4572	+	29.8543i	−1.63393	+	1.07309i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−52.1352	−	19.7052i	−1.86914	−	0.706467i
$779$		0			0
$780$		0			0
$781$	−30.4751	+	43.6635i	−1.09049	+	1.56240i
$782$		0			0
$783$		0			0
$784$	19.1605	+	20.4176i	0.684302	+	0.729199i
$785$		0			0
$786$		0			0
$787$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$787$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$788$	−4.04310	−	0.382871i	−0.144029	−	0.0136392i
$789$		0			0
$790$		0			0
$791$		−	28.6351i		−	1.01815i
$792$	−13.6318	−	24.6206i	−0.484386	−	0.874854i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$797$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$798$		0			0
$799$		0			0
$800$	2.20732	+	28.1980i	0.0780405	+	0.996950i
$801$		0			0
$802$	−33.8113	−	27.0926i	−1.19392	−	0.956672i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	28.9316	−	39.8210i	1.01718	−	1.40003i	0.103022	−	0.994679i	$-0.467149\pi$
$809$	28.9316	−	39.8210i	1.01718	−	1.40003i	0.914160	−	0.405353i	$-0.132851\pi$
$810$		0			0
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$	−27.4350	+	31.1084i	−0.962779	+	1.09169i
$813$		0			0
$814$	3.83624	−	10.7626i	0.134460	−	0.377230i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.79837	−	20.9232i	0.237265	−	0.730226i	−0.759548	−	0.650451i	$-0.774580\pi$
$821$	6.79837	−	20.9232i	0.237265	−	0.730226i	0.996813	−	0.0797750i	$-0.0254202\pi$
$822$		0			0
$823$	1.70206	−	1.23662i	0.0593301	−	0.0431058i	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	1.70206	−	1.23662i	0.0593301	−	0.0431058i	0.617055	+	0.786920i	$0.288326\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	35.5967	−	25.8626i	1.23782	−	0.899329i	0.240369	−	0.970682i	$-0.422732\pi$
$827$	35.5967	−	25.8626i	1.23782	−	0.899329i	0.997451	+	0.0713526i	$0.0227315\pi$
$828$	13.2243	−	7.81782i	0.459576	−	0.271688i
$829$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$829$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$		0			0
$841$	−26.2471	−	19.0696i	−0.905071	−	0.657573i
$842$	47.1146	−	12.8849i	1.62368	−	0.444042i
$843$		0			0
$844$	49.7055	−	29.3845i	1.71094	−	1.01146i
$845$		0			0
$846$		0			0
$847$	−28.0000	−	7.93725i	−0.962091	−	0.272727i
$848$	−4.56787	−	9.71568i	−0.156861	−	0.333638i
$849$		0			0
$850$		0			0
$851$	5.93185	+	1.92738i	0.203341	+	0.0660696i
$852$		0			0
$853$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$853$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$854$		0			0
$855$		0			0
$856$	5.44482	+	31.2439i	0.186100	+	1.06789i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	29.9741	+	45.6395i	1.02092	+	1.55449i
$863$	6.47214	+	4.70228i	0.220314	+	0.160068i	0.692468	−	0.721449i	$-0.256523\pi$
$863$	6.47214	+	4.70228i	0.220314	+	0.160068i	−0.472154	+	0.881516i	$0.656523\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−46.4198	+	35.0901i	−1.57468	+	1.19035i
$870$		0			0
$871$		0			0
$872$	43.7583	+	6.23897i	1.48184	+	0.211278i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	18.2668	+	56.2193i	0.616824	+	1.89839i	0.367885	+	0.929871i	$0.380082\pi$
$877$	18.2668	+	56.2193i	0.616824	+	1.89839i	0.248939	+	0.968519i	$0.419918\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−29.6654	−	1.40148i	−0.998886	−	0.0471903i
$883$	55.3577	−	17.9868i	1.86293	−	0.605304i	0.869072	−	0.494686i	$-0.164717\pi$
$883$	55.3577	−	17.9868i	1.86293	−	0.605304i	0.993863	−	0.110619i	$-0.0352832\pi$
$884$		0			0
$885$		0			0
$886$	56.9140	−	15.5648i	1.91206	−	0.522909i
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$	−22.0711	+	16.0356i	−0.740242	+	0.537818i
$890$		0			0
$891$	28.5585	+	8.68399i	0.956746	+	0.290924i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−23.9266	−	17.9866i	−0.799332	−	0.600890i
$897$		0			0
$898$	−48.3211	+	31.7352i	−1.61250	+	1.05902i
$899$		0			0
$900$	−22.5000	−	19.8431i	−0.750000	−	0.661438i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	5.25553	+	30.1577i	0.174796	+	1.00303i
$905$		0			0
$906$		0			0
$907$	−18.2132	+	25.0684i	−0.604760	+	0.832381i	−0.996134	−	0.0878507i	$-0.972000\pi$
$907$	−18.2132	+	25.0684i	−0.604760	+	0.832381i	0.391373	+	0.920232i	$0.372000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12.9443	−	9.40456i	0.428863	−	0.311587i	−0.352331	−	0.935875i	$-0.614611\pi$
$911$	12.9443	−	9.40456i	0.428863	−	0.311587i	0.781194	+	0.624288i	$0.214611\pi$
$912$		0			0
$913$		0			0
$914$	−6.52183	+	8.13918i	−0.215723	+	0.269220i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	34.1974	−	47.0687i	1.12807	−	1.55265i	0.336381	−	0.941726i	$-0.390797\pi$
$919$	34.1974	−	47.0687i	1.12807	−	1.55265i	0.791687	−	0.610927i	$-0.209203\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		−	12.1801i		−	0.400478i
$926$	−32.5329	−	1.53695i	−1.06910	−	0.0505073i
$927$		0			0
$928$	23.1843	−	37.7977i	0.761062	−	1.24077i
$929$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$929$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$930$		0			0
$931$		0			0
$932$	21.5426	+	36.4406i	0.705652	+	1.19365i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$937$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$938$	−13.8791	+	36.7206i	−0.453168	+	1.19897i
$939$		0			0
$940$		0			0
$941$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$941$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	1.69777	−	60.1000i	0.0551992	−	1.95402i
$947$			58.2065i			1.89146i	0.324956	+	0.945729i	$0.394650\pi$
$947$			58.2065i			1.89146i	−0.324956	+	0.945729i	$0.605350\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−46.2410	−	15.0246i	−1.49789	−	0.486694i	−0.558489	−	0.829512i	$-0.688619\pi$
$953$	−46.2410	−	15.0246i	−1.49789	−	0.486694i	−0.939402	+	0.342817i	$0.888619\pi$
$954$	10.6517	+	4.02597i	0.344862	+	0.130346i
$955$		0			0
$956$	−23.4229	+	5.23151i	−0.757551	+	0.169199i
$957$		0			0
$958$		0			0
$959$	−26.4993	−	36.4732i	−0.855708	−	1.17778i
$960$		0			0
$961$	9.57953	−	29.4828i	0.309017	−	0.951057i
$962$		0			0
$963$	−27.2142	−	19.7723i	−0.876965	−	0.637152i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			52.7587i			1.69661i	0.529511	+	0.848303i	$0.322376\pi$
$967$			52.7587i			1.69661i	−0.529511	+	0.848303i	$0.677624\pi$
$968$	30.9456	+	3.22033i	0.994629	+	0.103505i
$969$		0			0
$970$		0			0
$971$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$971$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$972$		0			0
$973$		0			0
$974$	15.3656	+	56.1858i	0.492347	+	1.80031i
$975$		0			0
$976$		0			0
$977$	44.0711	−	32.0196i	1.40996	−	1.02440i	0.416632	−	0.909075i	$-0.363210\pi$
$977$	44.0711	−	32.0196i	1.40996	−	1.02440i	0.993328	−	0.115321i	$-0.0367898\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−37.9284	+	27.5566i	−1.21096	+	0.879813i
$982$	22.0000	−	58.2065i	0.702048	−	1.85744i
$983$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$983$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	32.8202			1.04362
$990$		0			0
$991$	−24.0000			−0.762385			−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000			−0.762385			−0.381193	+	0.924496i	$0.624487\pi$
$992$		0			0
$993$		0			0
$994$	−32.9759	−	50.2102i	−1.04593	−	1.59257i
$995$		0			0
$996$		0			0
$997$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$997$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$998$	−0.323190	−	0.122154i	−0.0102304	−	0.00386673i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.b.349.1	yes	8
7.6	odd	2	CM	616.2.bi.b.349.1	yes	8
8.5	even	2		616.2.bi.a.349.2	yes	8
11.7	odd	10		616.2.bi.a.293.2	✓	8
56.13	odd	2		616.2.bi.a.349.2	yes	8
77.62	even	10		616.2.bi.a.293.2	✓	8
88.29	odd	10	inner	616.2.bi.b.293.1	yes	8
616.293	even	10	inner	616.2.bi.b.293.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.a.293.2	✓	8	11.7	odd	10
616.2.bi.a.293.2	✓	8	77.62	even	10
616.2.bi.a.349.2	yes	8	8.5	even	2
616.2.bi.a.349.2	yes	8	56.13	odd	2
616.2.bi.b.293.1	yes	8	88.29	odd	10	inner
616.2.bi.b.293.1	yes	8	616.293	even	10	inner
616.2.bi.b.349.1	yes	8	1.1	even	1	trivial
616.2.bi.b.349.1	yes	8	7.6	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41264 - 0.0667372i) q^{2} +(1.99109 + 0.188551i) q^{4} +(2.51626 + 0.817582i) q^{7} +(-2.80011 - 0.399234i) q^{8} +(2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(-1.41264 - 0.0667372i) q^{2} +(1.99109 + 0.188551i) q^{4} +(2.51626 + 0.817582i) q^{7} +(-2.80011 - 0.399234i) q^{8} +(2.42705 - 1.76336i) q^{9} +(0.0629004 + 3.31603i) q^{11} +(-3.50000 - 1.32288i) q^{14} +(3.92890 + 0.750845i) q^{16} +(-3.54623 + 2.32901i) q^{18} +(0.132447 - 4.68855i) q^{22} +2.56038 q^{23} +(-1.54508 - 4.75528i) q^{25} +(4.85595 + 2.10232i) q^{28} +(-2.42225 + 7.45492i) q^{29} +(-5.50000 - 1.32288i) q^{32} +(5.16497 - 3.05338i) q^{36} +(2.31678 + 0.752769i) q^{37} +12.8185 q^{43} +(-0.500000 + 6.61438i) q^{44} +(-3.61689 - 0.170873i) q^{46} +(5.66312 + 4.11450i) q^{49} +(1.86529 + 6.82061i) q^{50} +(-1.57760 - 2.17138i) q^{53} +(-6.71939 - 3.29390i) q^{56} +(3.91928 - 10.3695i) q^{58} +(7.54878 - 2.45275i) q^{63} +(7.68122 + 2.23580i) q^{64} -10.4916i q^{67} +(12.9884 + 9.43662i) q^{71} +(-7.50000 + 3.96863i) q^{72} +(-3.22254 - 1.21801i) q^{74} +(-2.55285 + 8.39541i) q^{77} +(10.3127 + 14.1942i) q^{79} +(2.78115 - 8.55951i) q^{81} +(-18.1079 - 0.855469i) q^{86} +(1.14774 - 9.31035i) q^{88} +(5.09796 + 0.482763i) q^{92} +(-7.72535 - 6.19024i) q^{98} +(6.00000 + 7.93725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9	\( 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9} + 4 q^{11} - 28 q^{14} - q^{16} - 3 q^{18} - 9 q^{22} + 16 q^{23} + 10 q^{25} - 7 q^{28} - 4 q^{29} - 44 q^{32} - 9 q^{36} + 30 q^{37} + 24 q^{43} - 4 q^{44} - 23 q^{46} + 14 q^{49} - 5 q^{50} + 50 q^{53} - 7 q^{56} + 2 q^{58} - 9 q^{64} + 48 q^{71} - 60 q^{72} - 28 q^{74} - 14 q^{77} + 40 q^{79} - 18 q^{81} - 12 q^{86} + 17 q^{88} - 24 q^{92} - 7 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9 + 4 * q^11 - 28 * q^14 - q^16 - 3 * q^18 - 9 * q^22 + 16 * q^23 + 10 * q^25 - 7 * q^28 - 4 * q^29 - 44 * q^32 - 9 * q^36 + 30 * q^37 + 24 * q^43 - 4 * q^44 - 23 * q^46 + 14 * q^49 - 5 * q^50 + 50 * q^53 - 7 * q^56 + 2 * q^58 - 9 * q^64 + 48 * q^71 - 60 * q^72 - 28 * q^74 - 14 * q^77 + 40 * q^79 - 18 * q^81 - 12 * q^86 + 17 * q^88 - 24 * q^92 - 7 * q^98 + 48 * q^99

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